00:01
Hi, so we have two questions here.
00:03
First one, we're solving for the rate constant for the decay process.
00:08
And remember that a decay process is a first -order reaction, so we will use this formula.
00:13
For first -order reaction, the rate constant is equivalent to ln of 2 divided by the half -life.
00:19
So let's plug in the value of half -life in the denominator.
00:23
We have 1 .90 times 10 to the power of 3 days.
00:27
Therefore, the rate constant is equivalent to 3 .65 times 10 to the negative 4th per day.
00:38
This is the rate constant.
00:41
And then let's solve for the number of years that it will take for the sample to decay to 1 fourth of the original concentration.
00:50
So for first -order reaction, the formula is y, the remaining amount is equivalent to y over the initial amount, multiplied by 2 raised to the power of negative t, the time elapsed over t, half -life.
01:00
So let's plug in the values that we have.
01:03
The remaining amount is 1 fourth of the initial amount.
01:06
We don't know the initial amount, so we're just going to write y0.
01:09
And then y0, the right side, multiplied by 2 raised to the power of negative t.
01:13
And then the half -life is 1 .90 times 10 to the power of 3 days.
01:18
So we can cancel y0 since we can just divide y0 on both sides of the equation...